An extension of LaSalle's invariance principle for discontinuous systems

In this paper, discontinuous righthand sides dynamical systems are considered. An extension of LaSalle invariance principle is presented by using locally Lipschitz continuous and nonpathological Lyapunnov functions. This result is used to locate chaotic attractors of studied systems, and less restrictive conditions are required. Numerical example has been given to illustrate the correctness of the theorem.